Homework

Chapter 3: Homework

6. Refer to the Kelson Sporting Equipment solved in Homework 2.

a) Determine and interpret the objective coefficient ranges

Standard objective coefficient range has an upper limit 9 (7.5+1.5) and has now lower limit (7.5- 1E+30).

Professional objective coefficient has no upper limit (9+1E+30) and has a lower limit of 7.5(9-1.5)

The coefficient ranges represent how much a coefficient can change without changing the optimal solution.

b) Determine and interpret the right-hand side ranges.

Frame right hand side range is 40 and 20 (30+10, 30-10)

Carbon right hand side range is 7 and 3 (6+1, 6-3)

The RHS range represents the range in which the shadow price is valid. For Frame and Carbon respectively, the range represents the range in which the shadow prices of 6.75 and 7.5 are valid.

c) How much will the value of the optimal solution improve if 20 extra hours of packaging and shipping time are made available?

20. Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank’s planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.

a) Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of lean in order to maximize the total

annual return for the new funds.

Let H be amount in home loans

P be amount in personal loans

And A be amount in auto loans

Maximize .07H+.12P+.09A

Subject to

H+P+A=1000000

H=>400000

P-0.06A0

b) How much should be allocated to each...